A computational method for solution of the prey and predator problem

Biazar, Jafar; Montazeri, Roya

doi:10.1016/j.amc.2004.05.001

Cited by 40 publications

(38 citation statements)

References 3 publications

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“…Foxes eat the rabbits and rabbits eat clover, and there is an increase and decrease in the number of foxes and rabbits [3,4,5,6,7]. Another example of the prey and predator problem is given in [15] in a lake there are two species of fish: A, which lives on plants of which there is a plentiful supply, and B (the predator) which subsists by eating A (the prey).…”

Section: The Prey and Predator Problemmentioning

confidence: 99%

“…Another example of the prey and predator problem is given in [15] in a lake there are two species of fish: A, which lives on plants of which there is a plentiful supply, and B (the predator) which subsists by eating A (the prey). For more details on the mathematical modeling leading to the following system of nonlinear equations, governing the problem; the readers can be found more details in [3,4,5,6,7,14,15,16].…”

Section: The Prey and Predator Problemmentioning

confidence: 99%

“…Also, Biazar and Montazeri [4] used the Adomian decomposition method (ADM) to solve this problem. Moreover, Biazar et al [5] have successfully implemented the power series method to compute an approximation to the solution of the this problem.…”

Section: The Prey and Predator Problemmentioning

confidence: 99%

“…On the other hand, the problem in which some rabbits and foxes are considered living together, where foxes eat the rabbits and rabbits eat clover, and there is an increase and decrease in the number of foxes and rabbits appears to be interesting for the researchers to solve it and find the exact solution and approximate solutions to this problem, see for examples [3,4,5,6,7].…”

Section: Introductionmentioning

confidence: 99%

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A reliable iterative method for solving the epidemic model and the prey and predator problems

AL-Jawary

2014

IJBAS

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In the present article, we implement the new iterative method proposed by Daftardar-Gejji and Jafari (NIM) [V. Daftardar-Gejji, H. Jafari, An iterative method for solving nonlinear functional equations, J. Math. Anal. Appl. 316 (2006) 753-763] to solve two problems; the first one is the problem of spread of a non-fatal disease in a population which is assumed to have constant size over the period of the epidemic, and the other one is the problem of the prey and predator. The results demonstrate that the method has many merits such as being derivative-free, overcome the difficulty arising in calculating Adomian polynomials to handle the nonlinear terms in Adomian Decomposition Method (ADM), does not require to calculate Lagrange multiplier as in Variational Iteration Method (VIM) and no needs to construct a homotopy as in Homotopy Perturbation Method (HPM). The results obtained are compared with the results by existing methods and prove that the presented method is very effective, simple and does not require any restrictive assumptions for nonlinear terms. The software used for the numerical calculations in this study was MATHEMATICA 8.0.

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Section: The Prey and Predator Problemmentioning

confidence: 99%

Section: The Prey and Predator Problemmentioning

confidence: 99%

Section: The Prey and Predator Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A reliable iterative method for solving the epidemic model and the prey and predator problems

AL-Jawary

2014

IJBAS

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show abstract

“…where x(t) and y(t) are respectively the populations of rabbits and the foxes at the time t. The problem was solved by Biazar and Montazeri [1] using Adomian decomposition method (ADM), Biazar [2] using power series method, Rafei [3] by variation iteration method (VIM) and Goh [4] useing multistage variation iteration method (MVIM). The motivation of this paper is to extend the analysis of the differential transformation method (DTM) to solve the prey and predator problem.…”

Section: Introductionmentioning

confidence: 99%